1 fly-by-wire control augmentation anthony a. lambregts faa chief scientific and technical adviser...
TRANSCRIPT
1
Fly-By-WireControl Augmentation
Anthony A. LambregtsFAA Chief Scientific and Technical Adviser for Flight Guidance and Control
Tel 425-917-6581
SEA Control & Guidance Systems CommitteeLake Tahoe March 1-3, 2006
2
Overview
Motivation for Fly-By-Wire Design Top Level FBW Design Requirements
Time domain based Handling Qualities FBW design issues/choices
Algorithm types, design issues Observations
Proposed systematic Design Process Static Inversion of Short Period dynamics Stability Augmentation; Command Response Shaping, Hold Examples: PRC/PAH and FPARC/FPAH; relationships
Primary Flight Display & Controller requirements
Conclusions
3
Motivation for Fly-By-Wire Design
Costs Reduction common flight deck/ Handling Qualities / Type Rating
pilot training maintenance and spare parts weight reduction aerodynamic performance optimization (aft CG)
Flight safety improvements – Envelope Protection Customer Appeal
4
Top Level FBW Design Objectives
Suitable handling qualities - all control tasks simplify pilot's control task reduce workload consistent throughout the flight envelope avoid PIO
Flight envelope protection: prevent stall, overspeed, excessive bank angles and nz
not get in pilot’s way, or compromise airplane performance
5
FBW Control System Architecture
throttle
actuator
engine
e
airplane
TFlightControlComputer
display
Interface
actuatorS
stick
feel system
trimup
down
Sensor data
6
FBW Design Issues
Control algorithm choice (C*, C*U, etc.) & details handling qualities; PIO prevention certification: e.g. speed stability or equivalent safety envelope protection implementation
mode changes for up and away and takeoff / landing
display requirements
Column & Wheel versus Sidestick – sensitivity, authority
Passive versus Active feel system - implications
Actuator requirements bandwidth; central or remote loop closure
7
FBW Control Algorithm Choices
Simple electrical signaling only (no augmentation) example: Embraer 170
Classical Stability Augmentation pitch rate, angle of attack feedbacks simple command signal path
Non-classical Stability and Command Augmentation pitch attitude (), nz , flight path angle (FPA) feedbacks
suppression of phugoid multiple feed forward signal paths; pilot out of the loop “hold” function examples: Pitch Rate Cmd/ Att Hold; C* & C*U; FPA RC/Hold
8
Basic FBW System ExampleEmbraer RJ-170 / DO-728 concept
stick
e
Air Data
ActuatorActuatorElectronics
Pos sensor
ModularAvionics Units
Passive Feel
Default Gains
IRU
Airspeed Gain SchedAOA limiting
default
Autopilotservo
clutch
Autopilot cmds
9
Control Algorithm Response Types
• classical unaugmented airplanes are some timers referred to as “Alpha-Command response type”:• FBW control augmentation algorithms often classified by response type:
• Alpha-Command• pitch rate command• nz-command• FPA-rate command• other, e.g. Pitch Attitude or FPA proportional command
• response type classification is not very meaningful, since actual response and HQ depend very much on design details e.g.
• short term versus long term characteristics• pilot out of the loop chararacteristics• non-classical feedbacks, e.g. , Az,V, Ax, FPA…• feed forward paths and dynamic elements
Assuming thrust is controlled to maintain speed: then all these are variations on the same theme!
10
Response Types(Basic, without response shaping details)
KS e cmd
K
Kqq
KS
q
e cmdKP
S
KI
Proportional cmd without hold
KS
q
e cmd
K Kq
“Classical” SP augmentation
Pitch Rate cmd with pseudo Pitch Att Hold
11
Basic C* and C*U Control Algorithms
Fff1
KI
Sactuator
engine
compensationVc o
gK t
S
throttle
trimup
down
Boeing
+_ +_
V(nz pilot)attitude corrected
q
++_ +
stick
FFcomp
e
T
Airpl
+
+
12
C* and C*U Attributes
• inspired by C* handling qualities criterion??• C* HQ criterion was shown to be unreliable (AFFDL TR 70-74)
• design issues:• complexity, many sensors & customization features
• Az –feedback requires attitude compensation• flight condition tuning
• integral control of multiple feedbacks causes drift of control reference when pilot out of the loop – requires pilot tweaking
• integral control of Az and results in Phugoid damping, speed divergence – requires tight thrust control - Authrottle preferred• C*U airspeed feedback “restores” classical phugoid, static speed & stick force stability : “more classical” response
• autothrottle ON: U (airspeed)feedback degrades control • if reference speed commands differ, control divergences
θ
13
C* and C*U Responses
14
• C* algorithm: • No Static Stability: Fstick /knot = 0• without thrust control, speed diverges monotonically – resulting in stall for low speed conditions: need speed envelope protection
• display of flight path acceleration helps in setting thrust • with closed loop thrust-speed control (manual or automatic) effect of speed dynamics on the pitch Attitude/FPA control is eliminated, yielding lower pilot workload and tighter FPA tracking• pilot’s task reduces to maneuver control only
• C*U algorithm:
• classical response with undamped phugoid requires pilot to stay in the loop to suppress phugoid and provide continuous compensatory tracking • same result can be achieved in a simpler way: using classical stability augmentation only
C* and C*U Additional Comments
15
C* Morphed into FPA rate cmd/hold
• responses identical to original C*, if gains are equivalent• fewer, simpler sensors• no pilot-out-of-the-loop control reference drift• still need extensive flight condition tuning• missing: integral control of -error
actu
engine
throttle
q
e
TAirplane
Kq
KFF
K
stick
γ
cmdγ
γK
+
Prefilter
KI
S_+ +_+_
16
Control Algorithm DesignConsiderations
What response characteristics are desirable? Classical Short Period augmentation only?
If yes, achievable HQ improvements limited! SP + Phugoid augmentation? Other? Which one, why?
Sensor requirements? Algorithm complexity,
Analyzability of “Higher order” design Applicability of classical Handling Qualities criteria use of “Equivalent Lower Order Systems”: problematic
Achieving good Handling Qualities still very difficult !
17
Handling Qualities
Definition: The conglomerate of characteristics and features that facilitate the execution of a specific flight control task; includes display and feel system!
• good HQ requires design attributes appropriate to control task (e.g. pitch attitude, FPA, or altitude control)
• each task has a finite time allotment or expectation for its completion (bandwidth requirement)
• direct control of “slow variables” requires special design attributes (e.g.FPA response augmentation & display)
• desired HQ and control harmony achieved when the pilot can execute the task without undue stress and high concentration effort, e.g. using interim innerloop(s) & control targets
18
Unaugmented SP Pitch Dynamics
q
2
t
qe
+++
1
1
2Se
Cm
Cm
yyI
cSq ..
qCm
+-
S
1
S
1
2SPSPSP
2
2SP2θ
ωSω2ζS
ω
S
K
eδ
θ .1Sτ
2=
VT*(CL)1g
g*CL =
2*(W/Sw)g**VT*CL
V-const:
19
FBW Control – Time Domain Response Attributes for good HQ
Harmonious response:1. Coordinated start-up2. Correct sensitivity (K )3. Low SS response lag 4. Minimal overshoot,5. Good Damping6. Short settling time
1
Time
Task VariableResponse
Input stick
KS
stick
2
3
46
5
Stick
20
Design Methodology- An Update -
Desired: • systematic/reliable process, producing desired results:• generalized/reusable design – minimal application & Flt Condition adaptation
Approach: Step 1: Stability Augmentation using Static Inversion
eliminates flight condition dependencies, gain schedules defines basic SP innerloop characteristics: ,
Step 2: Add Integral Feedback loop “retrims” airplane - eliminates SS command response droop
Step 3: Add Command Augmentation Feed Forward Paths shapes response to pilot control inputs, as desired provides “Hold” function for pilot established command
21
S
1
S
11S
1
2θτ +++
+
q_
Cm e
Cm
q
)(SGact -
I YYcS.
ec
Unaugmented Aircraft SP modelCmq
+--
Ce
m
1
Cmq
Cm
ec
SP model inversion
Outerloopcmd
q
+--
K q
K
New SPdesign
cS
I yy.
q
q_
Step 1: Static Inversion Based Stability Augmentation
22
Step 2: Add Integral ControlConcatenate the State Feedbacks
Airplane Dynamics reduced to series of integrators - feedback serves as new - feedback for S.P.
augmentation Integral feedback control eliminates SS response droop dropping loop gains by factor 4 for each state assures all
poles placed on real axes (>1); Alternatively, pole placement directly yields gains
S
1
S
1+-
+-+- S
K IqKK
cmd
Stripped SP
dynamics
New SP dynamics
1SK/1SKK/1SKKK/1
1
KKKSKKSKS
KKK
θ
θ
I2
θI3
qθIqθIqθ2
q3
qθI
cmd
23
0.382)(S1S2.618)(S
1
14S4SS
1
θ
θ23
cmd
Short Period dependency on and and q eliminated!
Example: K q= 4, K = 1, K I = .25
Step 3: Command Response Augmentation
To create classical transfer function
add forward loop integrator to realize K/S-like response
add 2nd order numerator, cancel one of denominator poles
Result:
stickθ/δ
1})S(1/K)SK(1/K)SKK{(1/K
1)SKS(K
S
K
δ
θ
I2
θI3
qθI
FFI2
FFPstick
stick
Step 2 cont’d :Pitch Rate Command / Attitude Hold
Algorithm (PRCAH)
2_
24
Step 3 cont’d :PRCAH Algorithm Implementation
controls (CAP)
controls SS -response lag (Drop Back),
relative to : actuator effect not considered (design to be minor)
FFPK 0t
FFIK
S
KK Istick
FFII KK /1
++-S
1 cmd
Augmented SP dynamics
22
2
2 SPSP
SP
SS
IKstickK
FFIK
FFPK
+ +stick S
1
2SPθq
SPSPq
ω.KK
ω2ζK
25
Step 3 cont’d :PRCAH Feed Forward Gains Determination
NumeratorTherefore KFFP = n1.n2 ; KFFP = n1 + n2
-Response lag determined by KFFI and KI : select , then: select KFFP to cancel “slowest” denominator pole,
associated with KI integral control feedback loop
Special Case 1: Design denominator to include pole with desired final ; Select and to cancel remaining poles: -response reduces to first order!
IFFI KK /1
FFIK FFPK
1.11 212 SSSKSK nnKKIFFP
26
Special Case 2: Design system to have the “ideal”
Classical SP form and response characteristics n , SP , SP :
This requires n1 = n and n2 = d
n fulfills the role of , but is not affected by flight condition
final algorithm is generalized, no Flt Cond dependencies, assuming constant is desired
Flt Cond adaptations handled in Static Inversion Module
1)S1}(τ)Sω/(2)S{(1/ω
1)S1)(τS(τ
S
K
1})S/ω(2ζ)S{(1/ω
1)S(τ
S
K
δ
θ
dSPSP22
SP
n2n1stick
SPSP22
SP
nstick
stick
Step 3 cont’d :PRCAH Feed Forward Gains Determination
2θτ
270 5 10 15 20 25
0
1
2
3
4
5
6
Time ~sec
Pitc
h R
ate,
Pic
h A
ttitu
de,
Thet
a C
md
~deg
.sec
, deg
Pitch Rate Cmd /Pich Att Hold Agorithm responsesKq = 4, Ktheta = 1, Ki = .25, Kffi = 3.5, Kffp = 2.309
Tautheta = .5 sec, no actuator dynamics
Pitch RatePitch AttitudePich Att Cmd
PRCAH Algorithm: Example Response 1
CAP = 2.309 (g/VT)
280 5 10 15 20 25
-1
0
1
2
3
4
5
6
Time ~sec
Pitc
h R
ate,
Pitc
h A
ttitu
de, P
ich
Att
Cm
d ~
deg/
sec,
deg
Pitch Rate Cmd / Pitch Att Hold Algorithm responsesKq = 4, Ktheta = 1, Ki = .25, Kffi = 5, Kffp = 6.236
Tautheta = -1, no actuator dynamics
Pitch RatePitch AttitudePitch Att Cmd
PRCAH Algorithm: Example Response 2
CAP = 6.236 (g/VT)
29
PRCAH AlgorithmFrequency Response
-200
-150
-100
-50
0
50
Pitch Rate cmd/Att Hold algorithm Kq=4, Ktheta=1, Ki=.25, Kstick =.1rad/sec/full stick
Frequency response Theta/stick ~rad/full stick
Mag
nitu
de
(dB
)
10-2
10-1
100
101
102
103
-360
-315
-270
-225
-180
-135
-90
-45
Pha
se (
de
g)
Frequency (rad/sec)
No Actuator
No Actuator
Attuator =1024/(S2+64S+1024)
Tautheta=-1
Tautheta=1
Tautheta=0
Tautheta=-1
Tautheta=0
Tautheta=1
30
PRCAH AlgorithmComments
• may be selected for the specific task, e.g. • for -control 0; for FPA control < 0
• Algorithm Feedback gains may be selected to support Autopilot outerloop modes• Feed Forward gains can compensate to a large extend to provide desired augmented manual responses• Not clear how to interpret CAP criteria, since ~ the same response characteristics can be achieved with different sets of feedback & feedforward gains, yielding different values for CAP, compare slide 27: CAP =2.309 (g/VT) and slide 31: CAP =1.73(g/VT)
• here CAP = (g/VT).KFFP.KI.K.Kq
31
0 5 10 15 20 25-1
0
1
2
3
4
5
6
Pitch Rate Cmd / Pitch Att Hold Control AlgorithmKq = 3, Ktheta = 1, Ki = .333, Kffi = 2.5, Kffp = 1.73
Tautheta = .5, No actuator dynamics
Time ~sec
Pitc
h R
ate
, P
ich
Att
itu
de,
Pit
ch A
tt c
md
~d
ed/s
ec,
deg
Pitch RatePich AttitudePich Att cmd
CAP = 1.73 (g/VT)
32
Flight Path Angle Rate Command / Hold (FPARCH) Algorithm
Direct FPA rate command and Hold control strategy is very attractive:
eliminates need for using iterative -control to satisfy higher order objective: reduces work pilot workload FPA will be maintained without pilot tweaking, regardless of speed & configuration changes, turbulence and windshear
facilitates altitude crossing at designated waypoints,
continuous descent procedures, final approach tracking HUD compatible
needs suitable display
33
FPA Rate Command / FPA HoldAlgorithm- System 1
++-S
1 cmd
Augmented SP dynamics
22
2
2 SPSP
SP
SS
IKstickK
FFIK
FFPK
+ +stick S
1
1
1
2S
K
-
FPA ()
αLCV .g.
)/.(2τ
.2θT
SW
, continuously computed on board
2SPθq
SPSPq
ω.KK
ω2ζK
34
FPA Rate Command / FPA HoldAlgorithm – System 1
IθqIγθqθθqq2
IθqFFI2
FFPstick
stick KKKSKKKK1)S)(τKKSKS(S
KK1)KSKS(K
S
K
δ
γ
2
Make , then transfer function becomes
, where is identical to TF on slide 23 !
Conclusion: FPARCH and PRCH algorithmscan provide identical and responses!
2θγ τK
1)S1}(τ)S(1/K)SK(1/K)SKK{(1/K
1)SKS(K
S
K
δ
γ
2θI2
Iθ3
Iθq
FFI2
FFPstick
stick
stick
stick
35
FPA Rate Command / FPA HoldAlgorithm – System 1
and in the numerator of can be
selected to satisfy two conditions: the desired response lag:
Thus, cancellation of one of the poles in the denominator;
Best strategy: cancel pole associated with
Example (next slide): and KFFI = 5
Then , and
Scheduling KFFI and KFFP with eliminates
response variability due to
FFIθIγ K)τ(1/Kτ2
stickδ
γFFIK FFPK
γθIFFI τ)τ(1/KK2
12 nFFIn τKτ 2ττ
21 θn 6.0.ττK
21 nnFFP
2θτ1τγ
2θτ
2θτ
36
0 5 10 15 20 250
1
2
3
4
5
6
FPA RAte Cmd /FPA Hold algorithm responsesKq = 4, Ktheta = 1, Ki = .25, Kffi = 5, Kffp = 6, Kstick = 5 deg/sec/full stick
Time ~sec
FP
A C
md,
FP
A,
Pic
h A
ttitu
de ~
deg
Pich AttitudeFPA FPA cmd
FPA Rate Command / FPA HoldAlgorithm-System1
Note: polecancelled
2
CAP = 6.0 (g/VT)
37
FPA Rate Command / FPA HoldAlgorithm-System1
-250
-200
-150
-100
-50
0
50
FPARCH algorithm Freq response FPA/dStick ~radians/unit Kq=4, Ktheta=1, Ki=.25, Kffi= 5, Kffp=6, Kstick=.1 rad/unit
Mag
nitu
de
(dB
)
10-2
10-1
100
101
102
103
-450
-405
-360
-315
-270
-225
-180
-135
-90
Pha
se (
de
g)
Frequency (rad/sec)
No Actuator
No Actuator
102464SS
1024:Actuator
2
Gain Margin ~27 db (factor ~22.5)
38
5 10 15 20 25 30 35
-1
0
1
2
3
4
Full Airplane Simulation with FPARCH algorithm step dStick=10%, Kstick=.0641 rad/sec/unit stick
Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft, Tauthetatwo=2 secKq=4,Ktheta=1, Ki=.25, Kffi=5, Kffp=6
Time ~seconds
FPA ~deg
FPAcmd ~deg
delta Pitch Att ~deg
delta-Trust/10000~lbs
Elevator ~deg
VE-error ~kn
FPA Rate Command / FPA HoldAlgorithm-System1
39
5 10 15 20 25 30 35-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Full Airplane Simulation with FPARCH algorithmTwin Jet, Weight 120,000 lbs, Ve=350 kn, Alt=25,000ft,
step dStick=10%, Kstick=.04475 rad/sec/unit stickKq=4, Ktheta=1,Ki=.25, Kffi=4.47, Kffp=4.411, Tauthetatwo=1.47 sec
Time ~seconds
FPA ~deg
FPAcmd ~deg
delta Pitch Att ~deg
delta-Trust/10000~lbs
Elevator ~deg
VE-error ~kn
5 10 15 20 25 30 35-4
-2
0
2
4
6
8
Full Airplane Sim FPARCH AlgorithmTwin jet Weight=100,000 lbs, Flaps Down, Gear down, Alt=10000 ft, Ve=127kn
step dStick=10%, Kstick=.1066 rad/sec/unit stick Kq=4, Ktheta=1, Ki=.25, Kffi=5.08, Kffp=6.243, Tauthetatwo=2.08 sec
Time ~seconds
FPA ~deg
FPAcmd ~deg
delta Pitch Att ~deg
delta-Trust/10000~lbs
Elevator ~deg
VE-error ~kn
FPA Rate Command / FPA HoldAlgorithm-System1
40
++-S
1 cmd
Augmented SP dynamics
22
2
2 SPSP
SP
SS
IKstickK
FFIK
FFPK
+ +stick S
1
1
1
2S
K
-
FPA ()
1)S(1/K)SK(1/K)SKK(1/K
1)SKS(K
S
K
δ
γ
I2
Iθ3
Iθq
FFI2
FFPstick
stick
Selecting 2 K
results in
Conclusion: response no longer a function of 2
FPA Rate Command/FPA HoldAlgorithm-system 2
41
FPA Rate Command/FPA HoldAlgorithm-System2
For System 2, only K needs to be adjusted for to maintain invariable response
KFFI and KFFP can be selected to cancel two poles, making the / cmd transfer function
first order (in this simplified SP approximation analysis)
2θτ
42
0 5 10 15 20 25-1
0
1
2
3
4
5
6
Timw ~sec
FP
A C
ms,
FP
A,
Pitc
h A
ttitu
de ~
deg,
Pitc
h R
ate
~de
g/se
c FPA Rate Cmd / FPA Hold algorithm responses (System 2)Kq = 4, Ktheta = 1, Ki = .25, Kffi = 3, Kffp = 1, Kstick = 5 deg/sec/full stick
Pitch AttitudeFPA FPA cmdPitch Rate
FPA Rate Command/FPA HoldAlgorithm-System2
/ cmd TFReduced toFirst Order
43
FPA Rate Command/FPA HoldDisplay Requirement
FPA must be displayed to allow pilot to close loop
on FPA FPA response delay cannot be reduced enough to
make display of “raw FPA” adequate A quicker responding display symbol is needed:
cmd developed in algorithm meets the need
display as a separate symbol blend with actual : CmdFPA
1Sγτ
SγτFPAFPA Quickened
If pilot closes loop on quickened he cannot induce PIO !!
44
Controller Authority &Sensitivity Scheduling
Airplane manuever authority (nz) is proportional to
Controller dead zones and command discontinuities must be avoided; maneuver command limit must
occur at controller displacement limit be matched to airplane maneuver authority
Controller sensitivity around neutral must be suitable
and sensitivity variation must be minimal
2
2
stallV
V
These requirements are difficult to reconcile with passive feel system, but its advantage is simplicity
45
Controller Authority & Sensitivity(Fixed Displacement)
.5 1
Nz - cmd
-.5-1
stick
2.5
0
2.0
1.5
-.5
Vmin = 1.07 Vstall
Ve =1.41 Vstall
Ve 1.58 Vstall
Authoritylimit
46
Final Algorithm & control System Implementation Details
• “Front-end” sensitivity scheduling:• need to assure pilot cannot command more than the airplane maneuver limits, to prevent stall and excessive nz
• “Tail-end” control surface command processing:• need to include software cmd rate and position limits, that correspond to actuator performance capability
• prevent command wind-up• minimize delay on control command reversal
• Assuming control surfaces are dimensioned correctly, then pilot + control algorithm should always operate within airplane performance capability and limits:
• Minimizes PIO susceptibility
47
Optimal Pilot Gain and Phase Compensation
• Optimal pilot phase compensation is assumed to be zero• Optimal pilot gain definition: Maximum gain the pilot can use in a continuous compensatory control tracking task, to get to his desired target as quick as possible, but without overshoot• Example:
• previous FPARCH algorithm (system 1)
5 10 15 20 25 30 35-4
-2
0
2
4
6
8
Time ~seconds
Full Airplane Simulation with FPARCH algorithm Twin jet 120,000 lbs, Ve=200kn, Alt=10,000 ft
closed loop response with pilot model Kp =4.7 units dStick/rad FPA-error Kq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tauthetatwo=2 sec
FPAcmd ~deg
FPA ~deg
Pitch Att ~deg
Elevator ~deg
FPA loop closureStep FPA tracking error=.1 rad
dStick
48
Loop Closure Options and Effects
5 10 15 20 25 30 35
-4
-2
0
2
4
6
8
Full Airplane Simulation with FPARCAH algorithm Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft
closed loop response with pilot model Kp=8 units dSick/rad FPAerrorKq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tauthetatwo=2 sec
Time ~seconds
FPAcmd ~deg
FPA ~deg
Pitch Att ~deg
Elevator ~deg
FPAcmd loop closureStep FPA tracking error=.1rad
dStick
5 10 15 20 25 30 35
-4
-2
0
2
4
6
8
Time ~seconds
Full Airplane Simulation wirh FPARCH algorithm Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft
closed loop response with pilot model Kp=8 units dStick/rad FPAerrorKq=4, Ktheta=1, Ki=.25 Kffi= 5, Kffp=6, Tauthetatwo=2
FPAcmd ~deg
FPA ~deg
Pitch Att ~deg
Elevator ~deg
FPAquickened loop closureStep FPA tracking error=.1 rad
dStick
49
PIO SusceptibilityGraceful stability Degradation
(No cliffs, No actuator rate & position limiting)
5 10 15 20 25 30 35-6
-4
-2
0
2
4
6
8
Time ~seconds
Full Airplane simulation with FPARCH algorithm Twin jet Weight=120,000 lbs, Ve=200 kn, Alt=10,000 ft
closed loop response with pilot gain Kp=15 units dStick/rad FPAerrorKq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tautheta2=2 sec
FPAcmd ~deg
FPA ~deg
Pitch Att ~deg
Elevator ~deg
Pitch Attitude loop closure
dStick ~units
5 10 15 20 25 30 35-8
-6
-4
-2
0
2
4
6
8
10
12
Full Airplane Simulation with FPARCH algorithmTwin jet Weight =120,000 lbs, Ve=200kn, Alt=10,000 ft
clossed loop response with pilot gain Kp=15 units dStick/rad FPAerrorKq=4, Ktheta=1, Ki=.25, Kffi=5, Kffp=6, Tauthetatwo=2 sec
Time ~seconds
FPAcmd ~deg
FPA ~deg
dPitch Att ~deg
Elevator ~deg
FPA loop closureStep FPA tracking error=.1 rad
dStick
50
Conclusions
Existing FBW control algorithms and design methodologies are complex, difficult to understand & analyze A new, simpler, more systematic methodology was discussed, consisting of three major design phases
static SP Airplane model inversion synthesis if new SP innerloop dynamics command response augmentation to satisfy HQ
Result: a generalized, flight condition independent design PRCAH and FPARCH algorithms can be designed to produce identical responses and HQ FPARCH algorithm requires display of quickened FPA